A metallic rod of length $$'\ell '$$ is tied to a string of length $$2$$$$\ell $$ and made to rotate with angular speed $$w$$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $$'B'$$ in the region, the $$e.m.f$$ induced across the ends of the rod is

A beam of unpolarised light of intensity $${{\rm I}_0}$$ is passed through a polaroid $$A$$ and then through another polaroid $$B$$ which is oriented so that its principal plane makes an angle of $${45^ \circ }$$ relative to that of $$A$$. The intensity of the emergent light is

A circular loop of radius $$0.3$$ $$cm$$ lies center of the small loop is on the axis of the bigger loop. The distance between their centers is $$15$$ $$cm.$$ If a current of $$2.0$$ $$A$$ flows through the smaller loop, than the flux linked with bigger loop is

Two short bar magnets of length $$1$$ $$cm$$ each have magnetic moments $$1.20$$ $$A{m^2}$$ and $$1.00$$ $$A{m^2}$$ respectively. They are placed on a horizontal table parallel to each other with their $$N$$ poles pointing towards the South. They have a common magnetic equator and are separated by a distance of $$20.0$$ $$cm.$$ The value of the resultant horizontal magnetic induction at the mid-point $$O$$ of the line joining their centres is close to $$\left( \, \right.$$ Horizontal component of earth's magnetic induction is $$3.6 \times 10.5Wb/{m^2})$$